CRYSTAL GROWTH & DESIGN
Induction Time as an Instrument to Enhance Comprehension of Protein Crystallization Andre´ Bernardo,† Carlos Eduardo Calmanovici,‡ and Everson Alves Miranda*,†
2004 VOL. 4, NO. 4 799-805
School of Chemical Engineering, State University of Campinas, Unicamp, P. O. Box 6066, CEP 13083-970 Campinas, SP, Brazil, and Rhodia Research Centre, Rhodia Brasil Ltda, Paulı´nia, Brazil Received September 12, 2003;
Revised Manuscript Received May 5, 2004
ABSTRACT: Protein crystallization is a subject in which the commonplace “more an art than a science” still survives, and in which crystallization and crystallography are still synonyms. One of the major hindrances has been the lack of thermodynamic and kinetic parameters required for efficient crystallization design. In this article, induction times for porcine insulin and hen egg-white lysozyme were measured by absorbance at 320 nm at different levels of supersaturation, pH, and temperature, allowing determination of nucleation kinetics and interfacial tension. These parameters can help in the design and control of crystallization systems. Moreover, nucleation is explained on the basis of electrostatic interactions, and interfacial tension is related to the zeta potential of protein particles. Introduction al.1
Ny´vlt et pointed to a preconceived expectation that acts as an obstacle to the study of crystallization. According to them, “The art and the science of crystallization often become interwoven making physicians, engineers, and sorcerers confused when talking about crystals. Thus, sorcerers publish their magic, physicians explain interatomic layers and engineers try to improve the production of crystalline products and design more efficient and economic industrial equipment”. Protein crystallization is a subject for which this still occurs, mainly because the thermodynamic and kinetic data used for crystallization design are scarce for proteins. Several articles have focused on nucleation as a possible way to better understand protein crystallization.2-5 One important parameter of crystal nucleation kinetics is the period of time between the attainment of supersaturation and the formation of critical nuclei, or embryos (clusters of freely aggregated molecules for which the probability of growing into crystals or being dissolved in the solution is the same). This time, defined as “real induction time” (t*), depends fundamentally on temperature and supersaturation.6 Nevertheless, t* cannot be experimentally measured, because it is not possible to detect critical nuclei formation; therefore, to obtain measurements, it is necessary to let these nuclei grow to a detectable size. Consequently, it is only possible to evaluate a period of time called “induction time” (tind), which is larger than t* and is defined as the period of time between the attainment of supersaturation and the first detectable changes in physical properties of the system due to formation of a new phase. Induction time cannot be considered a fundamental property of the system, since its value depends on the technique employed to detect formation of the new phase. However, analysis of the values for induction time can help comprehension of * To whom correspondence should be addressed. † State University of Campinas. ‡ Rhodia Research Centre.
mechanisms of new phase formation and growth from critical nuclei into crystals.7 Several methods have been used to measure induction time, from the simplest, visual inspection,8 to second harmonic generation,9 including light scattering,7,10-12 electronic microscopy,13 nuclear magnetic resonance,14 and fluorescence.15 Absorbance of ultraviolet radiation at 280 nm allows monitoring of the variation in protein concentration in solution16 and the detection of particulate material at 320 nm.17 Wilson et al.18 utilized absorbance at 350 nm to detect lysozyme induction time based on this principle. Nevertheless, despite the successful measurements of induction time in all these articles, induction time data are seldom used to determine crystallization design parameters. This article describes the efforts of engineers in the science of protein crystallization: determination of nucleation kinetics parameters relevant to crystallization system design and process control, with a glimpse at future industrial applications of protein crystallization. Induction time for insulin and lysozyme solutions at different levels of pH, supersaturation, and temperature was measured to determine nucleation kinetics as well as interfacial tension. The latter was correlated with the zeta potential of the proteins, which helped to achieve a better comprehension of the mechanism of protein particle formation and how it is related to electrostatic interaction in the media. Experimental Procedures Reagents. Porcine insulin (96.57% purity, according to supplier) was kindly donated by Biobra´s, Brazil. Hen egg-white lysozyme (purity of 99%, according to supplier) was purchased from Sigma, USA. Ultrapure water was obtained by utilizing Milli-Q from Millipore, USA. Anhydrous sodium acetate was purchased from Merck, Germany; sodium chloride was purchased from Labsynth, Brazil; and glacial acetic acid is from Ecibra, Brazil. Determination of Solubility. Solubility data were obtained by controlling the temperature of the protein powder (rhombohedral zinc-insulin and tetragonal hen egg white
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lysozyme) and the respective solvent system in a suspension under agitation for a period of time long enough to reach equilibrium (at least 24 h), i.e., when the protein concentration in solution held constant (absorbance measurements after this moment did not differ more than the spectrophotometer error). Protein concentration was measured by UV absorbance, according to the methodology described by Gehle and Schu¨gerl.17 Measurement of Induction Time by UV Absorbance. In a 3.0 mL quartz cuvette, kept in a spectrophotometer at constant temperature, a solution of porcine insulin of known concentration was added to 0.1 M sodium acetate solution with 7 wt % of sodium chloride at pH 10.0. Then 0.1 M acetic acid solution with 7 wt % of sodium chloride was added until a volume of 2.0 mL was obtained. The final solutions were at pH 6.59 and pH 5.50 and were supersaturated in insulin. For lysozyme, 1.0 mL of lysozyme solution in 0.05 M sodium acetate buffer at pH 3.5 or 4.0 and 1.0 mL of 0.05 M sodium acetate buffer with 20 wt % of sodium chloride were added to a quartz cuvette. The volume of the final solution was 2.0 mL with 10 wt % of sodium chloride at pH 3.5 or 4.0 and was supersaturated in lysozyme. The variation in absorbance at 320 nm with time was measured. For both insulin and lysozyme, induction time was the time interval from the attainment of supersaturation until an abrupt rise or disturbance in the absorbance profile occurred. Three solutions were measured simultaneously to obtain a mean and a standard deviation of measurements at the end of the experiment. Determination of Protein Zeta Potential. The zeta potentials of insulin and lysozyme suspensions were measured in 1.0 mM sodium chloride solution at different pH values using a Malvern Zetamaster S, England. This equipment detects the scattered light of a particle suspension (usually in the size range of 5-5000 nm) and converts the spectrum into particle velocity in the direction of an electric field. This particle movement is due to the presence of charge on the surface of individual particles.
Bernardo et al. Table 1. Solubility of Porcine Insulin as Function of pH and Temperature in 0.1 M Sodium Acetate Solution with 7% NaCl T (°C)
C* (mg/mL)
SDa (mg/mL)
3.23 5.50 5.50 5.50 6.59
25 15 25 35 25
0.121 0.918 0.626 0.301 0.186
0.006 0.205 0.025 0.095 0.015
a
Standard deviation.
Table 2. Porcine Insulin Induction Time as a Function of pH and Temperature in 0.1 M Sodium Acetate Solution with 7% NaCl at 25.0 °C C (mg/mL) 1.200 1.566 1.652 1.835 1.839 2.293 2.999 3.737 1.878 2.622 4.007 4.170 4.382
pH
meana (s)
SDb (s)
5.50 5.50 5.50 5.50 5.50 5.50 5.50 5.50 6.59 6.59 6.59 6.59 6.59
3133c
82 505 20d 563 506 79 28 51 34 20 112 146 20d
2517 2413 1583 1956 804 292c 230 1265 1148 1044 289 88
a Mean of three independent replicates. b Standard deviation. In this case, the mean corresponds to two different triplicates; d Half of the minor plot division, which in this case is equal to the graphic reading error. c
Table 3. Porcine Insulin Induction Time as a Function of Temperature at pH 5.50 and σ Equal to 1
Results and Discussion The studies of protein nucleation were done with insulin as well as lysozyme. There was an implicit logic in the choice of these two proteins. Crystallization of insulin has been studied for many years and has been used in its commercial purification ever since. Schlichtkrull19 cites the first insulin crystallization obtained by Abel in 1926 and the first insulin crystallization with zinc in 1929 by Hartig. Hen egg-white lysozyme is the most frequently used protein model in crystallization studies.20,21 Its thermodynamic data have generated several articlessits solubility curve is well defined.16,22-24 As solubility data on lysozyme were already known,23 it was possible to prepare solutions whose degree of supersaturation was known and to measure induction time by variation in absorbance at 320 nm with time according to the procedure already described. Studies on lysozyme nucleation were intended to be an extension of the databases which would enhance comprehension of the phenomena already observed in the insulin results, and all lysozyme results were processed in the same manner as the insulin data. Nucleation of Porcine Insulin. Induction time for insulin solutions at different degrees of supersaturation was measured as a function of pH and temperature. As solubility data for insulin are very scarce in the literature,19,25 it was necessary to obtain solubility data for the conditions used (Table 1). Solubility data allow determination of the degree of supersaturation, since protein concentration is known.
pH
T (°C)
meana (s)
SDb (s)
15.0 25.0 35.0
2345c
96 661 97
1729 603
a Mean of three independent replicates. b Standard deviation. In this case, the mean corresponds to two different triplicates.
c
Table 2 shows measurement of induction time at different concentrations, which are equivalent to different degrees of supersaturation, as a function of pH and temperature. Table 3 shows measurements of induction time at different concentrations and temperatures, which are equivalent to the same supersaturation degree. The variation in induction time tind with supersaturation can be used to distinguish between the two mechanisms of primary (homogeneous or heterogeneous) nucleation, in addition to allowing estimation of interfacial tension, using eqs 1 and 2 from the classical theory of nucleation, assuming a spherical nucleus (β ) 16.755) and a molecular volume of 7.80 × 10-3 m3/ mol for insulin.26 Plotting the logarithm of induction time as a function of the reciprocal of the square of logarithm of dimensionless supersaturation, it is possible to visualize two regions where data are distributed in the graph, which allows the plotting of two straight lines. The steeper one corresponds to homogeneous nucleation for which f is 1, and the value of interfacial tension is hence obtained. The other line corresponds to heterogeneous nucleation, for which f is less than 1.
Induction Time for Comprehension of Crystallization
log (ti) ) A + B)
B T (log S)2 3
βγ3ν2NAf (2.3R)3
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(1)
(2)
Figures 1 and 2 represent calculations in which eqs 1 and 2 were used for porcine insulin data at 25.0 °C and pH values of 5.50 and 6.59, respectively. A possible manner to explain Figures 1 and 2 is to say that at higher supersaturation values, the most significant phenomenon is the formation of a new surface (which prevails in homogeneous nucleation) and at lower supersaturation entropy (or molecule ordering) is preponderant (as occurs in heterogeneous nucleation, supported by an outer surface). However, a reservation must be made: the insulin buffer system from which the results were generated is the same for all measurements and therefore cannot generate a nucleation that is homogeneous and heterogeneous. It is more reasonable to say that the nucleation was heterogeneous (inevitable because of the solid surface of the cuvette and unrecognizable surfaces), but under some conditions it appeared homogeneous. At pH 5.50, the value of γS is 457 µJ/m2 and of f is 0.0510 (for heterogeneous nucleation). At pH 6.59, the value of γS is 2170 µJ/m2 and of f is 0.00567. Hunter27 defines zeta potential as the electric potential in the stagnant boundary layer or in the electric double layer. The zeta potential of a given particle in a dilute electrolyte medium tends toward the zeta potential at infinite dilution ζ0, which is an intrinsic property of the particle related to the charge distribution on the particle surface.28 The magnitude of the zeta potential is lower at pH 5.50 than at pH 6.59, indicating a greater tendency toward agglomeration at pH 5.50 (Figure 3). In addition, at pH 5.50 (insulin isoelectric point) the zeta potential was not equal to zero. Also, according to Hunter,27,28 this is relatively common for proteins and the main cause for this is the presence of impurities close to the protein particles. The interfacial tension rose almost five times between pH 5.50 and pH 6.59. This is probably because of electrostatic interactions. The isoelectric point (IEP) of insulin is 5.50, which means that at this pH the net electric charge of the molecule is null. Above the IEP, the net electric charge of the protein is positive, and therefore there is an electrostatic repulsion between the molecules. As interfacial tension can be interpreted as a resistance to formation of a surface unit (by nucleation), higher interfacial tension at pH 6.59 indicates greater resistance to introduction of area increments. Factor f indicates the degree of heterogeneity; the lower the f, the more heterogeneous is the nucleation. Hence, a lower f factor is associated with greater resistance to particle formation and a consequent nucleation aided by alien surfaces (as occurs in heterogeneous nucleation). At pH 6.59, electrostatic repulsion implicates that there is a higher requirement of alien surface interference in ordering the molecules that shape the nucleus. Zeta potential, an indication of potential magnitude at the beginning of diffuse double layer,23 is twice as large at pH 6.59 as at pH 5.50 (Figure 3). It is an
Figure 1. Variation in induction time with supersaturation for porcine insulin in 0.1 M sodium acetate solution with 7 wt % NaCl at pH 5.50 and 25.0 °C. The symbols 9 and b define lines associated with homogeneous and heterogeneous nucleation, respectively, as defined in the text.
Figure 2. Variation in induction time with supersaturation for porcine insulin in 0.1 M sodium acetate solution with 7 wt % NaCl at pH 6.59 and 25.0 °C. The symbols 9 and b indicate homogeneous and heterogeneous nucleation, respectively, as defined in the text.
additional indication that the electrostatic interactions are preponderant in the nucleation of insulin at pHs near IEP. Variation in induction time with supersaturation also allows calculation of nucleation kinetics utilizing the mononuclear approach (the mononuclear approach implies that the formation of the first nucleus is sufficient to break metastability29), according to eqs 3 and 4 (Figures 4 and 5).
tind )
1 JestV
J ) k N σn
(3) (4)
Figures 4 and 5 allow description of the nucleation rate of insulin in 0.1 M sodium acetate solution with 7 wt % NaCl at the two pH levels and 25.0 °C. At pH 5.50, the homogeneous nucleation rate (whose unit is no./(m3 s)) is 67.9σ2.3, whereas the heterogeneous nucleation rate
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Figure 3. Variation with pH at 25.0 °C of the zeta potential of porcine insulin in 1 mM NaCl solution. The null potential is at pH 4.5.
Bernardo et al.
Figure 6. Variation in nucleation rate with temperature in 0.1 M sodium acetate solution with 7 wt % NaCl at pH 5.50 and supersaturation σ of 1 (R2 ) 0.8966). Table 4. Lysozyme Induction Time as a Function of Temperature and pH in 0.05 M Sodium Acetate Solution with 10% NaCl C (mg/mL)
pH
T (°C)
meana (s)
SDb (s)
12.0 12.5 13.0 13.5 14.0 14.5 16.0 17.0 17.5 18.0 18.5 19.0 20.0
3.5 3.5 3.5 3.5 3.5 3.5 4.0 4.0 4.0 4.0 4.0 4.0 4.0
25 25 25 25 25 25 25 25 25 25 25 25 25
6083 5267 4605 4592 3931 3749 5072 3424 2510 4164 1972 2549 1615
486 250 273 1982 399 540 434 573 264 333 221 529 303
a
Figure 4. Nucleation kinetics of porcine insulin in 0.1 M sodium acetate solution (with 7 wt % NaCl at pH 5.50 and 25.0 °C). The symbols 9 and b indicate homogeneous and heterogeneous nucleation, respectively, as defined in the text.
Mean of three independent replicates. b Standard deviation.
(which expresses dependence on supersaturation) was larger for homogeneous nucleation for the two levels of pH. Nucleation activation energy was also calculated. It expresses the dependence of nucleation kinetics on temperature. It was hypothesized that the variation in nucleation with temperature obeys an Arrhenius-like equation, as in eq 5:
( )
kN ) k0N exp
Figure 5. Nucleation kinetics of porcine insulin in 0.1 M sodium acetate solution with 7 wt % NaCl at pH 6.59 and 25.0 °C. The symbols 9 and b indicate homogeneous and heterogeneous nucleation, respectively, as defined in the text.
is 162.2σ0.5. At pH 6.59, the homogeneous nucleation rate is 0.19σ3.0, whereas the heterogeneous nucleation rate is 220.5σ0.3. The nucleation constant was larger for heterogeneous nucleation and the nucleation index
-Eatt RT
(5)
The value of nucleation activation energy for insulin crystallization in 0.1 M sodium acetate solution with 7 wt % NaCl at pH 5.50, 50 kJ/mol, was calculated using data from Figure 6 and eq 5. The activation energy obtained from supersaturation under conditions such as nucleation could be defined as heterogeneous. It is, hence, activation energy of heterogeneous nucleation. From the activation energy, it is possible to obtain the variation in the heterogeneous nucleation kinetics obtained with temperature. Nucleation of Hen Egg-White Lysozyme. Unlike the case of insulin, solubility data for lysozyme are available in the literature.16,22-24 The solubility of lysozyme at 25.0 °C in 0.05 M acetate buffer (with 10 wt % NaCl it is 0.947 ( 0.071 mg/mL for pH 3.50 and 1.0 mg/mL for pH 4.0.23 Table 4 shows induction time measurements for different concentrations, which are equivalent to different degrees of supersaturation, as a
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Table 5. Lysozyme Induction Time in 0.05 M Sodium Acetate Solution with 10 wt % NaCl at pH 4.0 and σ ) 9.85
a
T (°C)
meana (s)
SD (s)
15 35
6966 1928
484 958
Mean of three independent replicates.
Figure 9. Nucleation kinetics of lysozyme in sodium acetate buffer 0.05 M with 10 wt % NaCl at 25.0 °C and pH 4.0.
Figure 7. Variation in induction time with supersaturation, which allows calculation of interfacial tension of lysozyme in sodium acetate buffer 0.05 M with 10 wt % NaCl at pH 4.0 and 25.0 °C.
Figure 10. Nucleation kinetics of lysozyme in sodium acetate buffer 0.05 M with 10 wt % NaCl at 25.0° and pH 3.5 °C.
Figure 11. Lysozyme zeta potential as a function of pH in 1 mM NaCl solution at 25.0 °C.
Figure 8. Variation in induction time with supersaturation, which allows calculation of interfacial tension of lysozyme in sodium acetate buffer 0.05 M with 10 wt % NaCl at pH 3.5 and 25.0 °C.
function of pH and temperature. Table 5 shows induction time measurements at different concentrations and temperatures, which are equivalent to the same degree of supersaturation. For lysozyme, the data are distributed in such way that it is possible to plot only one line (Figures 7 and 8). Therefore, eqs 1 and 2 were used only to calculate interfacial tension at pH 4.0 and pH 3.5 assuming that f factor was 1 (homogeneous nucleation). The calculated interfacial tensions at 25.0 °C were 197 and 265 µJ/m2 at pH 3.50 and pH 4.00, respectively. Calculations were made assuming a spherical nucleus (β of 16.755) and a molecular volume of 6.66 × 10-2 m3/ mol, calculated from growth unit dimensions.30 Inter-
facial tension values for lysozyme had the same bulk order as those for insulin. For lysozyme, higher interfacial tension at pH 4.00 than at pH 3.50 means a greater resistance to nuclei formation at this pH. Moreover, the nucleation kinetics of lysozyme at 25.0 °C was calculated using the same procedure as that used for the insulin data (Figures 9 and 10). Results of induction time measurement shown in Figures 9 and 10 allowed description of the nucleation kinetics of lysozyme at 25.0 °C. At pH 3.5 the nucleation rate (whose unit is no./(m3 s)) is 0.29σ2.3 and at pH 4.0 it is 0.00026σ4.7. There was a strong dependence of nucleation rate on supersaturation at pH 4.0. As data for lysozyme induction time were determined in a region far from lysozyme’s IEP, the importance of electrostatic interaction can be better understood by measuring zeta potential (Figure 11). Electrostatic interactions play an important role in the nucleation of lysozyme, although different from that in the nucleation of insulin: the lower interfacial tension value, which means low resistance to introduction of a
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Crystal Growth & Design, Vol. 4, No. 4, 2004 Table 6. Interfacial Tension as Function of Zeta Potential protein
pH
ζ (mV)
γS (µJ/m2)
lysozyme lysozyme insulin insulin
3.50 4.00 5.50 6.59
21.5 13.7 -24.2 -50.2
197 265 457 2170
Bernardo et al.
physical chemistry of the science of crystallization, nor does it require more art than science to study their crystallization. Calculated nucleation rates and interfacial tensions are comparable with values calculated for small molecules.31 Quite simple measurements such as UV absorbance and zeta potential allow the expansion of knowledge of protein crystallization, as well as determination of parameters that help to design and control crystallization systems. The surface charge of proteins is an important factor affecting their nucleation. Symbols and Abbreviations A B
Figure 12. Interfacial tension as a function of zeta potential in 1.0 mM sodium chloride solutions for the two proteins.
new surface, corresponds to a pH farther from the IEP, with higher zeta potential, which means a higher surface charge (at pH 3.5). The activation energy of lysozyme was also estimated utilizing eq 5 and data from Table 5. Its value was 33 kJ/mol, comparable to the activation energy of insulin. Influence of Electrostatic Interactions on the Formation of Protein Nuclei. The influence of electrostatic attractions was shown to be the determining factor in the nucleation of the proteins under study. This can be observed when the calculated interfacial tensions and the zeta potential measured under the different conditions are compared (Table 6 and Figure 12). The relationship between the resistance to introduction of a new surface (interfacial tension) and the surface charge of particles (zeta potential) does not seem to be limited to simple electrostatic repulsion. Lysozyme at pH 3.5 and insulin at pH 5.5 have magnitudes of zeta potential very close to each other, but interfacial tension that are very different. The nature of the protein must be taken into account. Nevertheless, the zeta potential sign, positive or negative, seems to have some influence on the magnitude of the interfacial tension. From Figure 12, an equation that relates interfacial tension with the zeta potential of the proteins can be fitted:
log(γS) ) 2.5497-0.0131ξ
R2 ) 0.9025
The relevance of the above equation is that it provides evidence for the role of electrostatic interactions in protein nucleation. Although this equation was obtained from data on only two proteins, estimation of a thermodynamic parameter by use of a trivial measurement technique provides an incentive for seeking relationships such as this in protein crystallization, such as those already existing for simpler molecules (the relationship between interfacial tension and inorganic salt solubility31). Conclusions Proteins are very complex molecules, but knowledge of their complexity does not require changes in the
IEP J Jest kN n NA R S SD T t* tind
linear coefficient of eq 1 constant which is part of the angular coefficient of eq 1 and depends on interfacial tension of the system solute concentration in the system (mg/mL) equilibrium concentration of solute in the system (mg/mL) activation energy of nucleation (kJ/mol) factor of 1 for homogeneous nucleation and less than 1 for heterogeneous nucleation isoelectric point nucleation rate (no./(m3s)) stationary nucleation rate (no./(m3s)) nucleation constant (no./(m3s)) order of nucleation Avogadro number (6.022 × 1023 mol-1) gas constant (8.3145 J/(mol K)) adimensional supersaturation (C/C*) standard deviation absolute temperature (K) real induction time (s) induction time (s)
Greeks β γS σ ζ
shape factor, 16π/3 for spheres interfacial tension (J/m2) relative supersaturation ((C - C*)/C*) zeta potential (mV)
C C* Eatt f
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CG034170+
